The likely defeat of the boundary changes by Labour and the Lib Dems means the Tories will need a lead of seven points to win a majority in 2015.

Conservative and Liberal Democrat ministers will vote against each other for the first time since the coalition was formed when parliament votes on the boundary changes later today. Photograph: Getty Images.

Update: MPs have voted in favour of delaying the boundary changes to 2018 by 334 to 292.

Labour, the Lib Dems, the nationalist parties and at least four Conservatives[3] (David Davis, Philip Davies, Richard Shepherd and John Baron) voted in favour of the rebel amendment.

Barring any last-minute upset, the Conservatives' proposed boundary changes will finally receive their last rites in the Commons this afternoon. MPs will vote on a Labour amendment to delay the reforms until 2018 and, without the support of the Lib Dems, who will fulfil their pledge[4] to oppose the changes in revenge for the abandonment of House of Lords reform, there is no hope of the Tories preventing defeat.

In addition to Labour and the Lib Dems, at least two Conservative MPs - Glyn Davies[5] and Philip Davies[6] - are likely to rebel, with David Davis also considering[7] voting against the changes (an assortment of rebels that suggests the whips should also keep a close eye on David Davies[8]). Thus, even if the Tories succeed in winning the support of the eight DUP MPs (the SNP is expected to abstain[9]), they will be well short of the numbers needed to save the reforms. As David Cameron's official spokesman delicately put it yesterday, "clearly, from the Prime Minister's perspective, the arithmetic looks pretty difficult".

The defeat of the changes means it will be all but impossible for the Conservatives to win a majority in 2015. Under the existing boundaries, and assuming a Lib Dem vote of around 15 per cent, the Tories require[10] a lead of seven points to win an overall majority, compared to a lead of four points under the new boundaries. Labour, by contrast, needs a lead of just one point to win a majority under the current system, compared to a lead of three points under the new boundaries.

The party's advantage is partly due to differential constituency sizes, a factor that the boundary changes, which would have fixed constituency sizes at plus or minus five per cent of 76,000 voters, were designed to mitigate. Since Labour tends to perform best in smaller, urban seats, while the Tories perform best in larger, rural seats, it takes an average[11] of 33,470 votes to elect a Labour MP, compared to an average of 35,030 to elect a Conservative one (and 119,944 to elect a Lib Dem, which is why they bang on about electoral reform).

But even with the boundary changes, Miliband's party would still have enjoyed a significant advantage over its opponents. This is because the the electoral bias towards Labour owes more to differential turnout (fewer people tend to vote in Labour constituencies) and regional factors (the Tory vote is poorly distributed) than it does to unequal constituencies. As a report[12] by the University of Plymouth concluded: "The geography of each party's support base is much more important, so changes in the redistribution procedure are unlikely to have a substantial impact and remove the significant disadvantage currently suffered by the Conservative Party."

By 2015, as the Tories struggle to even remain the single largest party (something that will require a lead of four points), the more reflective Conservative MPs might ask themselves whether it was worth sacrificing the boundary changes for the sake of preventing an elected House of Lords. When I interviewed former Conservative education secretary Kenneth Baker earlier this month[13], he told me that he regarded Cameron's failure to secure the boundary changes as his "biggest mistake". ConservativeHome editor Tim Montgomerie has described[14] the defeat of the reforms as the Tories' "worst single electoral setback since Black Wednesday".

Note the date - 29 January 2013 - it may well be remembered as the day that the Tories' hopes of outright victory in 2015 finally ended.